And no:
In[1]:= InverseFourierSequenceTransform[1, x, n, FourierParameters -> {a, 1}]
Out[1]= InverseFourierSequenceTransform[1, x, {-0.00913271, 0.0914715},
FourierParameters -> {{1.95061, 1.19098}, 1}]
and so not yes
In[2]:= InverseFourierSequenceTransform[1, x, n, FourierParameters -> {a, 2 Pi}]
Out[2]= InverseFourierSequenceTransform[1, x, {-0.00913271, 0.0914715},
FourierParameters -> {{1.95061, 1.19098}, 2 \[Pi]}]
In[3]:= $Version
Out[3]= "10.4.1 for Microsoft Windows (64-bit) (April 11, 2016)"